Science China Information Sciences

, Volume 53, Issue 9, pp 1727–1737 | Cite as

A centrality measure based on spectral optimization of modularity density

  • LiDong Fu
  • Lin Gao
  • XiaoKe Ma
Research Papers


Centrality analysis has been shown to be a valuable method for the structural analysis of complex networks. It is used to identify key elements within networks and to rank network elements such that experiments can be tailored to interesting candidates. In this paper, we show that the optimization process of modularity density can be written in terms of the eigenspectrum of kernel matrix. Based on the eigenvectors belonging to the largest eigenvalue of kernel matrix, we present a new centrality measure that characterizes the contribution of each node to its assigned community in a network, called modularity density centrality. The measure is illustrated and compared with the standard centrality measures by using respectively an artificial example and a classic network data set. The statistical distribution of modularity density centrality is investigated by considering large computer generated graphs and two large networks from the real world. Experimental results show the significance of the proposed approach.


centrality modularity density centrality kernel matrix eigenspectrum 


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Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.School of Computer Science and EngineeringXidian UniversityXi’anChina
  2. 2.College of ComputerXi’an University of Science and TechnologyXi’anChina

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